12a
0133
(K12a
0133
)
A knot diagram
1
Linearized knot diagam
3 5 8 6 2 12 11 4 7 1 9 10
Solving Sequence
9,11 4,12
8 3 7 10 1 6 5 2
c
11
c
8
c
3
c
7
c
9
c
12
c
6
c
4
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.85504 × 10
788
u
124
+ 3.67648 × 10
789
u
123
+ ··· + 1.84177 × 10
788
b − 7.07747 × 10
788
,
− 2.43301 × 10
788
u
124
+ 5.11381 × 10
789
u
123
+ ··· + 9.20887 × 10
787
a + 7.40748 × 10
788
,
u
125
− 21u
124
+ ··· − 3u + 1i
I
u
2
= h−u
5
b + 2u
5
+ u
3
b − 3u
3
+ b
2
− bu − b + 3u + 1, a, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 137 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−1.86 × 10
788
u
124
+ 3.68 × 10
789
u
123
+ · · · + 1.84 × 10
788
b − 7.08 ×
10
788
, −2.43 × 10
788
u
124
+ 5.11 × 10
789
u
123
+ · · · + 9.21 × 10
787
a + 7.41 ×
10
788
, u
125
− 21u
124
+ · · · − 3u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
4
=
2.64203u
124
− 55.5313u
123
+ ··· + 19.1899u − 8.04385
1.00720u
124
− 19.9616u
123
+ ··· + 5.57665u + 3.84275
a
12
=
1
u
2
a
8
=
0.481862u
124
− 11.4373u
123
+ ··· + 6.21816u − 7.95654
0.193276u
124
− 3.35222u
123
+ ··· − 2.51683u + 3.74346
a
3
=
5.54735u
124
− 116.372u
123
+ ··· + 44.2277u − 12.9410
0.987816u
124
− 19.2874u
123
+ ··· + 3.17753u + 5.56318
a
7
=
0.675138u
124
− 14.7895u
123
+ ··· + 3.70134u − 4.21308
0.193276u
124
− 3.35222u
123
+ ··· − 2.51683u + 3.74346
a
10
=
−0.0738144u
124
+ 1.46614u
123
+ ··· − 0.540455u + 1.43814
0.581451u
124
− 12.1584u
123
+ ··· + 2.87063u − 1.11559
a
1
=
−0.0738144u
124
+ 1.46614u
123
+ ··· − 0.540455u + 1.43814
−0.669841u
124
+ 14.0038u
123
+ ··· − 3.04870u + 1.19955
a
6
=
0.110132u
124
− 3.63794u
123
+ ··· + 3.70815u − 7.34491
−0.00891814u
124
+ 0.907468u
123
+ ··· − 4.09245u + 4.45700
a
5
=
6.04837u
124
− 126.686u
123
+ ··· + 46.7051u − 14.3744
1.25389u
124
− 24.7312u
123
+ ··· + 4.66284u + 5.75382
a
2
=
1.97982u
124
− 43.5856u
123
+ ··· + 16.2112u − 16.0378
−1.16126u
124
+ 25.5464u
123
+ ··· − 13.1425u + 10.4296
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.99618u
124
− 67.3888u
123
+ ··· + 57.9690u − 28.9195
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
125
+ 41u
124
+ ··· − 145u − 1
c
2
, c
5
u
125
+ 7u
124
+ ··· − 9u − 1
c
3
, c
8
u
125
− u
124
+ ··· + 20480u − 4096
c
6
u
125
+ 9u
124
+ ··· + 391375u + 25489
c
7
u
125
+ 3u
124
+ ··· − 6561489u + 604147
c
9
u
125
− 9u
124
+ ··· − 3u + 1
c
10
, c
12
u
125
+ 3u
124
+ ··· + 17u − 1
c
11
u
125
− 21u
124
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
125
+ 93y
124
+ ··· + 5099y −1
c
2
, c
5
y
125
+ 41y
124
+ ··· − 145y −1
c
3
, c
8
y
125
− 65y
124
+ ··· + 301989888y −16777216
c
6
y
125
− 127y
124
+ ··· + 36942460527y −649689121
c
7
y
125
− 91y
124
+ ··· − 24775319389441y −364993597609
c
9
y
125
+ 21y
124
+ ··· − 9y −1
c
10
, c
12
y
125
− 83y
124
+ ··· − 17y −1
c
11
y
125
− 3y
124
+ ··· − 17y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.655767 + 0.724024I
a = 0.33434 + 1.55566I
b = 0.447793 − 1.297880I
6.22986 + 11.45440I 0
u = −0.655767 − 0.724024I
a = 0.33434 − 1.55566I
b = 0.447793 + 1.297880I
6.22986 − 11.45440I 0
u = 0.800249 + 0.648673I
a = −0.435423 − 0.783872I
b = 0.0861307 + 0.1080150I
1.30610 − 5.13081I 0
u = 0.800249 − 0.648673I
a = −0.435423 + 0.783872I
b = 0.0861307 − 0.1080150I
1.30610 + 5.13081I 0
u = −0.812584 + 0.469650I
a = 0.404002 − 0.446533I
b = 0.205603 − 0.077552I
−1.40641 + 1.21884I 0
u = −0.812584 − 0.469650I
a = 0.404002 + 0.446533I
b = 0.205603 + 0.077552I
−1.40641 − 1.21884I 0
u = −0.556208 + 0.736230I
a = −0.28352 − 1.68148I
b = −0.372160 + 1.230560I
7.45341 + 5.28303I 0
u = −0.556208 − 0.736230I
a = −0.28352 + 1.68148I
b = −0.372160 − 1.230560I
7.45341 − 5.28303I 0
u = −0.906987 + 0.030403I
a = 0.519200 − 0.675115I
b = −0.025247 − 0.165447I
−3.11701 + 0.35524I 0
u = −0.906987 − 0.030403I
a = 0.519200 + 0.675115I
b = −0.025247 + 0.165447I
−3.11701 − 0.35524I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.149600 + 0.349509I
a = −0.535012 + 0.432272I
b = 0.078999 − 0.123440I
0.35042 − 8.49800I 0
u = 1.149600 − 0.349509I
a = −0.535012 − 0.432272I
b = 0.078999 + 0.123440I
0.35042 + 8.49800I 0
u = 0.601239 + 0.510683I
a = −0.62073 + 1.55220I
b = 0.094233 − 1.338300I
3.00041 − 8.24027I 0
u = 0.601239 − 0.510683I
a = −0.62073 − 1.55220I
b = 0.094233 + 1.338300I
3.00041 + 8.24027I 0
u = −0.874574 + 0.851604I
a = −0.310901 − 0.625158I
b = −1.21137 + 2.18977I
−1.140860 + 0.185574I 0
u = −0.874574 − 0.851604I
a = −0.310901 + 0.625158I
b = −1.21137 − 2.18977I
−1.140860 − 0.185574I 0
u = −0.081636 + 0.769248I
a = −0.36800 + 1.57288I
b = 0.83539 − 1.84910I
4.79797 + 5.99082I 0
u = −0.081636 − 0.769248I
a = −0.36800 − 1.57288I
b = 0.83539 + 1.84910I
4.79797 − 5.99082I 0
u = 1.079040 + 0.584332I
a = 0.456985 − 0.442276I
b = 0.69928 + 2.28590I
2.34856 − 1.43127I 0
u = 1.079040 − 0.584332I
a = 0.456985 + 0.442276I
b = 0.69928 − 2.28590I
2.34856 + 1.43127I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.012937 + 0.762843I
a = 0.34464 − 1.56179I
b = −0.79362 + 1.73569I
5.39776 + 0.24395I 0
u = −0.012937 − 0.762843I
a = 0.34464 + 1.56179I
b = −0.79362 − 1.73569I
5.39776 − 0.24395I 0
u = 0.465870 + 1.150330I
a = 0.562053 − 1.160690I
b = 0.54269 + 1.53375I
12.64840 − 1.23482I 0
u = 0.465870 − 1.150330I
a = 0.562053 + 1.160690I
b = 0.54269 − 1.53375I
12.64840 + 1.23482I 0
u = 0.709846 + 0.224075I
a = −0.52362 + 1.38728I
b = −0.080817 − 0.223298I
−2.63980 − 3.08960I 0
u = 0.709846 − 0.224075I
a = −0.52362 − 1.38728I
b = −0.080817 + 0.223298I
−2.63980 + 3.08960I 0
u = 0.514320 + 0.536168I
a = 0.57898 − 1.61891I
b = −0.187141 + 1.327970I
3.99062 − 2.47202I 0
u = 0.514320 − 0.536168I
a = 0.57898 + 1.61891I
b = −0.187141 − 1.327970I
3.99062 + 2.47202I 0
u = 0.720998 + 0.172200I
a = 0.469048 − 0.594384I
b = −0.36139 + 2.83331I
2.22327 − 1.42836I 0
u = 0.720998 − 0.172200I
a = 0.469048 + 0.594384I
b = −0.36139 − 2.83331I
2.22327 + 1.42836I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.426109 + 1.187070I
a = −0.238651 − 0.571154I
b = −0.405811 + 1.274680I
0.652314 + 1.029720I 0
u = 0.426109 − 1.187070I
a = −0.238651 + 0.571154I
b = −0.405811 − 1.274680I
0.652314 − 1.029720I 0
u = 0.458876 + 0.536127I
a = 0.452310 + 0.035894I
b = −0.825132 − 0.578278I
1.92047 + 0.80353I 0
u = 0.458876 − 0.536127I
a = 0.452310 − 0.035894I
b = −0.825132 + 0.578278I
1.92047 − 0.80353I 0
u = 1.212330 + 0.482011I
a = 0.510598 − 0.206916I
b = −0.0951467 + 0.0676096I
0.64386 − 3.59414I 0
u = 1.212330 − 0.482011I
a = 0.510598 + 0.206916I
b = −0.0951467 − 0.0676096I
0.64386 + 3.59414I 0
u = 0.571989 + 1.185410I
a = −0.521400 + 1.090710I
b = −0.58676 − 1.63613I
12.7252 − 7.6247I 0
u = 0.571989 − 1.185410I
a = −0.521400 − 1.090710I
b = −0.58676 + 1.63613I
12.7252 + 7.6247I 0
u = 0.916959 + 0.954823I
a = 0.457245 − 0.773326I
b = 1.04744 + 2.04862I
2.84396 − 4.99238I 0
u = 0.916959 − 0.954823I
a = 0.457245 + 0.773326I
b = 1.04744 − 2.04862I
2.84396 + 4.99238I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.564784 + 0.344975I
a = 1.98382 + 0.30021I
b = −1.97480 − 0.78752I
5.73499 − 7.52961I 0
u = −0.564784 − 0.344975I
a = 1.98382 − 0.30021I
b = −1.97480 + 0.78752I
5.73499 + 7.52961I 0
u = 1.098570 + 0.780864I
a = 0.586410 + 0.267127I
b = −0.1161610 − 0.0423086I
−1.27865 − 7.70761I 0
u = 1.098570 − 0.780864I
a = 0.586410 − 0.267127I
b = −0.1161610 + 0.0423086I
−1.27865 + 7.70761I 0
u = −0.569229 + 0.272964I
a = −2.03944 − 0.26318I
b = 2.11744 + 0.68360I
6.52143 − 1.68218I −4.62817 − 7.60476I
u = −0.569229 − 0.272964I
a = −2.03944 + 0.26318I
b = 2.11744 − 0.68360I
6.52143 + 1.68218I −4.62817 + 7.60476I
u = −0.863415 + 1.085210I
a = 0.673655 − 0.289380I
b = 0.458382 + 0.152113I
0.76237 + 1.42438I 0
u = −0.863415 − 1.085210I
a = 0.673655 + 0.289380I
b = 0.458382 − 0.152113I
0.76237 − 1.42438I 0
u = −1.373220 + 0.195922I
a = 0.628799 + 0.082468I
b = 0.071598 + 0.187138I
−0.67458 + 2.99174I 0
u = −1.373220 − 0.195922I
a = 0.628799 − 0.082468I
b = 0.071598 − 0.187138I
−0.67458 − 2.99174I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.472217 + 0.389380I
a = 1.12716 + 1.98262I
b = 0.589186 − 0.812623I
−0.34954 + 4.52947I 2.00000 − 13.81389I
u = −0.472217 − 0.389380I
a = 1.12716 − 1.98262I
b = 0.589186 + 0.812623I
−0.34954 − 4.52947I 2.00000 + 13.81389I
u = 0.941617 + 1.043060I
a = −0.835809 − 0.412754I
b = 0.144449 + 0.087004I
5.23935 − 6.54595I 0
u = 0.941617 − 1.043060I
a = −0.835809 + 0.412754I
b = 0.144449 − 0.087004I
5.23935 + 6.54595I 0
u = −1.21916 + 0.74148I
a = −0.605742 + 0.193847I
b = −0.245807 − 0.160971I
−4.30119 + 2.18209I 0
u = −1.21916 − 0.74148I
a = −0.605742 − 0.193847I
b = −0.245807 + 0.160971I
−4.30119 − 2.18209I 0
u = 0.97414 + 1.07043I
a = −0.384349 + 0.846825I
b = −0.80389 − 2.10781I
5.74950 − 9.66103I 0
u = 0.97414 − 1.07043I
a = −0.384349 − 0.846825I
b = −0.80389 + 2.10781I
5.74950 + 9.66103I 0
u = 0.343667 + 0.427238I
a = −2.27849 + 1.08888I
b = −0.583367 − 0.463637I
1.78016 − 4.49817I 8.2687 + 15.7325I
u = 0.343667 − 0.427238I
a = −2.27849 − 1.08888I
b = −0.583367 + 0.463637I
1.78016 + 4.49817I 8.2687 − 15.7325I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.408496 + 0.362667I
a = 0.956928 + 0.805869I
b = 1.56321 − 0.83191I
−0.66370 + 2.83474I 3.37234 − 5.05490I
u = −0.408496 − 0.362667I
a = 0.956928 − 0.805869I
b = 1.56321 + 0.83191I
−0.66370 − 2.83474I 3.37234 + 5.05490I
u = 1.02185 + 1.06029I
a = 0.832160 + 0.354664I
b = −0.151510 − 0.078925I
4.53531 − 12.42450I 0
u = 1.02185 − 1.06029I
a = 0.832160 − 0.354664I
b = −0.151510 + 0.078925I
4.53531 + 12.42450I 0
u = −0.045042 + 0.518697I
a = 0.82086 − 2.89616I
b = 0.050949 + 0.729389I
4.64685 + 0.82915I 22.7383 − 3.4399I
u = −0.045042 − 0.518697I
a = 0.82086 + 2.89616I
b = 0.050949 − 0.729389I
4.64685 − 0.82915I 22.7383 + 3.4399I
u = −0.92818 + 1.15242I
a = 0.277979 + 0.678887I
b = 0.83742 − 2.07441I
1.20280 + 4.30451I 0
u = −0.92818 − 1.15242I
a = 0.277979 − 0.678887I
b = 0.83742 + 2.07441I
1.20280 − 4.30451I 0
u = 0.472978 + 0.216290I
a = −1.03307 + 1.75271I
b = 0.086430 − 0.953078I
−2.31917 − 2.48205I −2.69773 + 2.44933I
u = 0.472978 − 0.216290I
a = −1.03307 − 1.75271I
b = 0.086430 + 0.953078I
−2.31917 + 2.48205I −2.69773 − 2.44933I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43892 + 0.34979I
a = −0.635403 + 0.009303I
b = −0.110646 − 0.197389I
−0.90323 − 2.21060I 0
u = −1.43892 − 0.34979I
a = −0.635403 − 0.009303I
b = −0.110646 + 0.197389I
−0.90323 + 2.21060I 0
u = −0.112927 + 0.503855I
a = −0.69615 + 1.51978I
b = 1.62571 − 2.00477I
−0.39162 + 1.59192I 5.69392 − 11.13943I
u = −0.112927 − 0.503855I
a = −0.69615 − 1.51978I
b = 1.62571 + 2.00477I
−0.39162 − 1.59192I 5.69392 + 11.13943I
u = 0.100372 + 0.504572I
a = −2.49644 − 1.62571I
b = 0.102842 + 0.125100I
4.17272 − 2.48498I 20.8404 + 8.1724I
u = 0.100372 − 0.504572I
a = −2.49644 + 1.62571I
b = 0.102842 − 0.125100I
4.17272 + 2.48498I 20.8404 − 8.1724I
u = −0.206853 + 0.453051I
a = 3.10944 − 0.25342I
b = −0.071875 − 0.135036I
3.28804 + 3.77271I 16.3017 − 14.4940I
u = −0.206853 − 0.453051I
a = 3.10944 + 0.25342I
b = −0.071875 + 0.135036I
3.28804 − 3.77271I 16.3017 + 14.4940I
u = 1.09874 + 1.02810I
a = 0.305533 − 0.805877I
b = 0.75512 + 2.32378I
1.03911 − 12.82610I 0
u = 1.09874 − 1.02810I
a = 0.305533 + 0.805877I
b = 0.75512 − 2.32378I
1.03911 + 12.82610I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.02955 + 1.12530I
a = −0.673996 + 0.265111I
b = −0.405078 − 0.208746I
0.16327 + 6.85626I 0
u = −1.02955 − 1.12530I
a = −0.673996 − 0.265111I
b = −0.405078 + 0.208746I
0.16327 − 6.85626I 0
u = 1.19774 + 0.96859I
a = 0.403750 + 0.508853I
b = 0.09110 − 1.49370I
4.58964 − 0.88814I 0
u = 1.19774 − 0.96859I
a = 0.403750 − 0.508853I
b = 0.09110 + 1.49370I
4.58964 + 0.88814I 0
u = 0.260833 + 0.364385I
a = 0.242358 + 1.026030I
b = 0.75167 − 4.05520I
1.72895 + 2.62928I 4.2210 + 23.6665I
u = 0.260833 − 0.364385I
a = 0.242358 − 1.026030I
b = 0.75167 + 4.05520I
1.72895 − 2.62928I 4.2210 − 23.6665I
u = 0.117927 + 0.423401I
a = 0.08943 − 2.01381I
b = −0.646164 + 1.045010I
1.45688 − 0.48467I 7.00982 + 0.32488I
u = 0.117927 − 0.423401I
a = 0.08943 + 2.01381I
b = −0.646164 − 1.045010I
1.45688 + 0.48467I 7.00982 − 0.32488I
u = 0.89351 + 1.28706I
a = 0.546290 − 0.344120I
b = 1.20226 + 1.43579I
1.67799 + 4.80704I 0
u = 0.89351 − 1.28706I
a = 0.546290 + 0.344120I
b = 1.20226 − 1.43579I
1.67799 − 4.80704I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.289466 + 0.319128I
a = 2.06945 + 0.68682I
b = −2.29689 − 1.76507I
−0.01102 − 2.45400I −3.8556 − 17.4577I
u = −0.289466 − 0.319128I
a = 2.06945 − 0.68682I
b = −2.29689 + 1.76507I
−0.01102 + 2.45400I −3.8556 + 17.4577I
u = 0.000211 + 0.414859I
a = 1.90598 − 0.30272I
b = 0.052743 − 0.664474I
1.04154 + 2.17510I 2.60677 − 4.61609I
u = 0.000211 − 0.414859I
a = 1.90598 + 0.30272I
b = 0.052743 + 0.664474I
1.04154 − 2.17510I 2.60677 + 4.61609I
u = 1.10596 + 1.14827I
a = −0.380345 − 0.527519I
b = −0.14580 + 1.46076I
4.41420 + 4.52899I 0
u = 1.10596 − 1.14827I
a = −0.380345 + 0.527519I
b = −0.14580 − 1.46076I
4.41420 − 4.52899I 0
u = −1.19012 + 1.07024I
a = −0.239452 − 0.671390I
b = −0.71402 + 2.29942I
−3.00982 + 6.94600I 0
u = −1.19012 − 1.07024I
a = −0.239452 + 0.671390I
b = −0.71402 − 2.29942I
−3.00982 − 6.94600I 0
u = 1.20410 + 1.08346I
a = −0.523565 + 0.396835I
b = −0.93756 − 1.71294I
5.22915 + 1.86813I 0
u = 1.20410 − 1.08346I
a = −0.523565 − 0.396835I
b = −0.93756 + 1.71294I
5.22915 − 1.86813I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.209563 + 0.308025I
a = −2.32011 − 0.47996I
b = 0.101894 + 0.624284I
0.62427 − 2.85549I 1.37496 + 1.53556I
u = 0.209563 − 0.308025I
a = −2.32011 + 0.47996I
b = 0.101894 − 0.624284I
0.62427 + 2.85549I 1.37496 − 1.53556I
u = 1.15661 + 1.15539I
a = −0.272255 + 0.878161I
b = −0.57135 − 2.24988I
8.4195 − 13.4799I 0
u = 1.15661 − 1.15539I
a = −0.272255 − 0.878161I
b = −0.57135 + 2.24988I
8.4195 + 13.4799I 0
u = −0.349753
a = −2.60555
b = 3.51569
3.09971 −30.1780
u = 1.20165 + 1.13913I
a = 0.250319 − 0.871083I
b = 0.54221 + 2.29559I
7.2064 − 19.5482I 0
u = 1.20165 − 1.13913I
a = 0.250319 + 0.871083I
b = 0.54221 − 2.29559I
7.2064 + 19.5482I 0
u = −0.300177 + 0.088480I
a = −0.35751 + 2.68856I
b = 0.74972 − 4.46124I
2.45673 − 2.54518I −37.1451 − 19.2544I
u = −0.300177 − 0.088480I
a = −0.35751 − 2.68856I
b = 0.74972 + 4.46124I
2.45673 + 2.54518I −37.1451 + 19.2544I
u = −0.40301 + 1.63903I
a = 0.289221 + 0.698596I
b = 0.59506 − 1.70803I
6.19530 + 3.43221I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.40301 − 1.63903I
a = 0.289221 − 0.698596I
b = 0.59506 + 1.70803I
6.19530 − 3.43221I 0
u = −0.24324 + 1.68667I
a = −0.290978 − 0.690325I
b = −0.55589 + 1.65264I
5.75964 − 2.41343I 0
u = −0.24324 − 1.68667I
a = −0.290978 + 0.690325I
b = −0.55589 − 1.65264I
5.75964 + 2.41343I 0
u = −1.27621 + 1.32563I
a = 0.245667 + 0.705611I
b = 0.56630 − 2.16228I
3.88678 + 7.08241I 0
u = −1.27621 − 1.32563I
a = 0.245667 − 0.705611I
b = 0.56630 + 2.16228I
3.88678 − 7.08241I 0
u = −1.35656 + 1.29152I
a = −0.236619 − 0.708219I
b = −0.53245 + 2.20027I
2.84254 + 12.99610I 0
u = −1.35656 − 1.29152I
a = −0.236619 + 0.708219I
b = −0.53245 − 2.20027I
2.84254 − 12.99610I 0
u = 1.73826 + 0.84266I
a = −0.532828 + 0.456968I
b = −0.56195 − 1.70610I
9.42374 + 0.00303I 0
u = 1.73826 − 0.84266I
a = −0.532828 − 0.456968I
b = −0.56195 + 1.70610I
9.42374 − 0.00303I 0
u = 1.80162 + 0.72379I
a = 0.529086 − 0.466468I
b = 0.50669 + 1.71976I
8.75351 − 5.95447I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.80162 − 0.72379I
a = 0.529086 + 0.466468I
b = 0.50669 − 1.71976I
8.75351 + 5.95447I 0
u = 1.18926 + 1.57654I
a = −0.581652 + 0.385364I
b = −0.87584 − 1.36218I
8.74385 + 4.24214I 0
u = 1.18926 − 1.57654I
a = −0.581652 − 0.385364I
b = −0.87584 + 1.36218I
8.74385 − 4.24214I 0
u = 1.10974 + 1.65453I
a = 0.590549 − 0.378019I
b = 0.88783 + 1.29999I
7.89271 + 10.20530I 0
u = 1.10974 − 1.65453I
a = 0.590549 + 0.378019I
b = 0.88783 − 1.29999I
7.89271 − 10.20530I 0
17
II. I
u
2
= h−u
5
b + 2u
5
+ · · · − b + 1, a, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
4
=
0
b
a
12
=
1
u
2
a
8
=
0
u
a
3
=
0
b
a
7
=
u
u
a
10
=
−u
3
−u
3
+ u
a
1
=
−u
3
−u
5
+ u
3
− u
a
6
=
u
3
u
5
− u
3
+ u
a
5
=
−u
5
b − u
4
b + 2u
3
b − bu + b
u
3
b + 2b
a
2
=
−u
3
−2u
5
+ 2u
3
+ b − 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 4u
5
b + u
4
b − 4u
5
− 9u
3
b + 7u
4
+ 3u
2
b + 7u
3
+ 5bu − 11u
2
− 3b − u + 6
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
3
, c
8
u
12
c
6
, c
9
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
c
7
, c
12
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
10
, c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
6
c
3
, c
8
y
12
c
6
, c
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
7
, c
10
, c
11
c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 0
b = 0.861379 − 0.162890I
−1.89061 − 1.10558I −1.04064 + 1.99047I
u = −1.002190 + 0.295542I
a = 0
b = −0.289622 + 0.827421I
−1.89061 + 2.95419I −3.79900 − 4.11613I
u = −1.002190 − 0.295542I
a = 0
b = 0.861379 + 0.162890I
−1.89061 + 1.10558I −1.04064 − 1.99047I
u = −1.002190 − 0.295542I
a = 0
b = −0.289622 − 0.827421I
−1.89061 − 2.95419I −3.79900 + 4.11613I
u = 0.428243 + 0.664531I
a = 0
b = 0.74515 + 1.88172I
1.89061 + 2.95419I 11.02954 − 8.16480I
u = 0.428243 + 0.664531I
a = 0
b = 1.25704 − 1.58618I
1.89061 − 1.10558I −0.484082 + 0.231437I
u = 0.428243 − 0.664531I
a = 0
b = 0.74515 − 1.88172I
1.89061 − 2.95419I 11.02954 + 8.16480I
u = 0.428243 − 0.664531I
a = 0
b = 1.25704 + 1.58618I
1.89061 + 1.10558I −0.484082 − 0.231437I
u = 1.073950 + 0.558752I
a = 0
b = 0.446919 + 0.343418I
− 3.66314I −2.53591 + 3.55776I
u = 1.073950 + 0.558752I
a = 0
b = −0.520868 + 0.215334I
− 7.72290I 2.83009 + 4.64337I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = 0
b = 0.446919 − 0.343418I
3.66314I −2.53591 − 3.55776I
u = 1.073950 − 0.558752I
a = 0
b = −0.520868 − 0.215334I
7.72290I 2.83009 − 4.64337I
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
6
)(u
125
+ 41u
124
+ ··· − 145u − 1)
c
2
((u
2
+ u + 1)
6
)(u
125
+ 7u
124
+ ··· − 9u − 1)
c
3
, c
8
u
12
(u
125
− u
124
+ ··· + 20480u − 4096)
c
5
((u
2
− u + 1)
6
)(u
125
+ 7u
124
+ ··· − 9u − 1)
c
6
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
· (u
125
+ 9u
124
+ ··· + 391375u + 25489)
c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
· (u
125
+ 3u
124
+ ··· − 6561489u + 604147)
c
9
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
)(u
125
− 9u
124
+ ··· − 3u + 1)
c
10
((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
125
+ 3u
124
+ ··· + 17u − 1)
c
11
((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
125
− 21u
124
+ ··· − 3u + 1)
c
12
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
)(u
125
+ 3u
124
+ ··· + 17u − 1)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
6
)(y
125
+ 93y
124
+ ··· + 5099y −1)
c
2
, c
5
((y
2
+ y + 1)
6
)(y
125
+ 41y
124
+ ··· − 145y −1)
c
3
, c
8
y
12
(y
125
− 65y
124
+ ··· + 3.01990 × 10
8
y −1.67772 × 10
7
)
c
6
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
125
− 127y
124
+ ··· + 36942460527y −649689121)
c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
125
− 91y
124
+ ··· − 24775319389441y −364993597609)
c
9
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
125
+ 21y
124
+ ··· − 9y −1)
c
10
, c
12
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
)(y
125
− 83y
124
+ ··· − 17y −1)
c
11
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
)(y
125
− 3y
124
+ ··· − 17y −1)
24
